Final answer:
There can be 22,100 different 5-card hands dealt that contain both jokers when two jokers are added to a standard 52-card deck.
Step-by-step explanation:
To calculate how many 5-card hands can be dealt containing both jokers from a 52-card deck plus two jokers, we follow these steps:
- First, we must place both jokers into our hand as they must be included.
- There are now 3 remaining spots in our hand and 52 cards in the deck to choose from, since we've included the two jokers in the total count.
- Therefore, we can use the combination formula, which is C(n, k) = n! / (k! * (n - k)!), where n is the number of items to choose from, k is how many to choose, and ! denotes factorial.
- Plug the numbers into the formula: C(52, 3) = 52! / (3! * (52 - 3)!) = (52 * 51 * 50) / (3 * 2 * 1) = 22,100.
Thus, we can deal 22,100 different 5-card hands containing both jokers.